A Family of Concepts of Dependence for Bivariate Distributions

Abstract

A family of concepts of stochastic dependence for bivariate distribution functions is introduced. Each concept gives rise to a family of bivariate distribution functions. We show the equivalence of some of these families with families of positively dependent distribution functions, which are known in the literature, and characterize some of them by notions from reliability theory. Interrelations among the various families are studied, and some moment inequalities are derived. Some examples and applications are discussed.

Key Words:

• Positive dependence
• Total Positivity
• Hazard rate
• Mean residual life
• Absolutely monotone functions